Different concentrations of ions on either side of a cell membrane constitute a concentration cell, which is described by the Nernst equation given below.What is the electrochemical potential across a membrane when the sodium ion concentration is 0.10 M on one side of the membrane and 0.010 M on the other side, and the temperature is 37°C body temperature) ?
(Given: Na⁺+e^- $\rightarrow$ Na, Eº_red = -2.71 V; F = 96,500 C; 1 J = 1 C V; R =8.315 J / mol K) )
E =E° = InQ

Question

Different concentrations of ions on either side of a cell membrane constitute a concentration cell, which is described by the Nernst equation given below.What is the electrochemical potential across a membrane when the sodium ion concentration is 0.10 M on one side of the membrane and 0.010 M on the other side, and the temperature is 37°C body temperature) ?
(Given: Na⁺+e^-

\rightarrow

Na, Eº_red = -2.71 V; F = 96,500 C; 1 J = 1 C V; R =8.315 J / mol K) )
E =E° = InQ

Quizplus · Accepted Answer

The Nernst equation at body temperature (37°C) for sodium ions (Na+) can be used to calculate the electrochemical potential across a membrane. The equation in its general form is E = E° - (RT/nF)ln([Na+]outside/[Na+]inside), where E° is the standard electrode potential, R is the gas constant (8.315 J/mol·K), T is the temperature in Kelvin (310 K for 37°C), n is the charge on the ion (which is +1 for Na+), and F is the Faraday constant (96,485 C/mol). Since E° for Na+ is not given and typically not needed for concentration cells, and assuming the question intends for us to calculate the potential difference due to concentration gradient only, we simplify the equation to E = -(RT/nF)ln([Na+]outside/[Na+]inside). Plugging in the values, including converting the temperature to Kelvin and using the natural logarithm, we find the potential difference to be approximately 61.5 mV, indicating that the correct answer is A. This calculation demonstrates how the concentration gradient of ions across a membrane can create an electrochemical potential, which is fundamental to many biological processes, including nerve impulse transmission.

Different Concentrations of Ions on Either Side of a Cell →\rightarrow→

Different Concentrations of Ions on Either Side of a Cell $\rightarrow$